带有时滞的反应扩散Hopfield神经网络的Hopf分岔

Hopf Bifurcation of Reaction-diffusion Hopfield Neural Network with Time Delay

将线性化理论应用于Hopfield神经网络模型,得到了它在非负平衡点的线性化方程。借助偏泛函微分方程理论和幂级数展开方法将该模型的线性化方程转化为代数方程,并借助笛卡尔符号法则和Routh-Hurwitz定理研究了该模型的非负平衡点的稳定性。以时滞为参数导出了存在Hopf分岔的条件。

The linearization theory is applied to Hopfield neural network model,and its linearization equation at non-negative equilibrium point is obtained.The linearized equations of the model are transformed into algebraic equations with the help of partial functional differential equation theory and power series expansion method,and the stability of the model’s non-negative equilibrium point is studied with the help of Descartes’rule of signs and Routh-Hurwitz theorem.The conditions for the existence of Hopf bifurcation are derived with time delay as parameters.